Presently, there are amusement park rides that vertically move a rider and have some kind of imagery that the rider is capable of viewing while on the ride. An example of such a ride is the “Tower of Terror” ride at various Disney amusement parks. In this ride, a rider is disposed on an elevator that moves between the floors of a haunted hotel. When the elevator stops at a particular floor, the rider is exposed to the “haunted” imagery associated with that floor. For example, the rider may be exposed to ghosts of prior denizens of the hotel where the images of the ghosts are generated using the “Pepper's Ghost” effect. Another type of amusement park ride endeavors to make the rider feel as if the rider is participating in the imagery that is being displayed on a screen by employing actuators to move the rider's chair and the rider relative to a platform in a manner that is synchronized with the imagery being displayed on a screen visible to the rider. By moving the rider in this manner, the rider believes that they are experiencing the forces that the rider would experience if actually participating in the scene being displayed. The actuators used to move the rider's chair are limited to a relatively small range of motion, typically, no more than about 24 inches. As such, many of these rides employ movement techniques that “trick” the rider's mind into believing that they are experiencing movements and forces commensurate with the image being viewed on the screen that are significantly greater than the movements and forces that the actuators are actually capable of generating. For instance, if the image being displayed on the screen is of the cockpit of a fighter jet that is banking into a turn, the chair actuators can be used to tilt the chair and thereby cause the rider to believe that they are in the cockpit of the jet and making the turn. However, if the actuator cannot tilt the chair far enough to reasonably reflect the degree to which the jet fighter is banking, the ride may tilt the image of the banking jet being displayed on the screen in the opposite direction from which the chair is being tilted. This typically “tricks” the rider's mind into believing that they are in the jet fighter and making the steep banking turn being displayed on the screen.